For what it's worth, I think you must have never been questioned critically when traveling alone or as a passport and separate eTA forcouple with an infant or toddler. Probably possession of the child if you intend to+ the child's ID and travel by air. The Canadian page saysdocuments everyone needs an eTA(passport/eTA and I believe that requires a passport. You do the latter by applying on behalf of your child. At least one airline says they will refuse boarding without both of those documentsbirth certificate) is more than adequate.
Also note thatBy the way, make sure you must have a ticket for the child, even for babes in arms,infant- it is required for international flights even when the babe-in-arms does not occupy his or her own seat. TheyThere may charge taxesbe some cost involved for that- I recall being hit by that when I took my (then) infant son to the UK.